(1+z)(5z+7)=0

Solution for (1+z)(5z+7)=0 equation:

(1+z)(5z+7)=0

We add all the numbers together, and all the variables

(z+1)(5z+7)=0

We multiply parentheses ..

(+5z^2+7z+5z+7)=0

We get rid of parentheses

5z^2+7z+5z+7=0

We add all the numbers together, and all the variables

5z^2+12z+7=0

a = 5; b = 12; c = +7;
Δ = b2-4ac
Δ = 122-4·5·7
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2}{2*5}=\frac{-14}{10}
=-1+2/5
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2}{2*5}=\frac{-10}{10}
=-1
$